'Naomi Wolf’s comments say that all the women who contacted me during those awful weeks – to say that they had suffered the same, had been silenced, driven underground by fear – were wrong. That they were letting the movement down.' Photograph: Tom Pietrasik

I led a campaign this year asking the Bank of England to keep a woman on its banknotes. Following its success, I was treated to a tour of the dark depths of Twitter, which unleashed a torrent of graphic and violent rape and death threats upon me.

In an interview, Naomi Wolf referred to this, implying that I had retreated to my "parlour" when things got "difficult". This irritated me because the one thing I didn't do was retreat. In fact, I did exactly what Wolf says I should have done. I did "lean in". I did adopt my warrior pose. And my God, did I shout back. I shouted, I screamed, I yelled, I bloody pushed. And then I broke, which is why I came off Twitter for most of September. I don't think having a breakdown was a good outcome.

The other day, I read a brilliant article in Wired by Laura Hudson, called Die Like a Man: The Toxic Masculinity of Breaking Bad. The name says it all really. To be a man in Breaking Bad you keep pushing, you keep providing, dominating, overpowering. Until you break. Until you die. And it's not just in Breaking Bad. Yes, the show takes it to extremes, but this is a masculinity we all recognise. And it's one that is celebrated. It's one that is contrasted with the pussydom of femininity.

And this is the problem with Wolf's comments – and comments like hers. They leave no room for humanity. Those words say that all the women who contacted me during those awful weeks, to say that they had suffered the same, to say that they had been silenced, that they had been driven underground by fear, those words say that those women were wrong. That they were weak. That they were letting the movement down. So Wolf's words aren't feminist.

Strong claim, I know. But to be fair to Wolf, it's an easy trap to fall into. It's the trap of a society that says to be a man you have to be inhuman. It's the trap of a society that places that inhuman masculinity on the highest pedestal we have. And it's a trap that feminists should be trying to avoid.

Wolf is right to say that feminists will come in for abuse. We always have, and until we live in an equal society, we always will. But she is wrong to imply that we should therefore just suck it up. She's wrong because it's defeatist: we should be outraged by abuse. We should flag it up, say it's wrong, challenge it, try to stop it. But more than this, she's wrong because sucking it up is part of that privileging of a masculinity that doesn't even serve men, let alone women.

As a society we need to grow up and get out of the playground. There is nothing inherently admirable about refusing to acknowledge emotion and psychological limitations. We all have them – to deny them, as Wolf's way of thinking does, is not only unhealthy, it's also unrealistic. And it's egotistical.

Part of the point of having a feminist movement rather than a feminist solo enterprise is that it's not just about one person's drive for success, glory and power. It's about all of us standing together and fighting. And you know what that means? It means that when one of us falls, when one of us needs a time-out, when one of us has led a battle and is under attack, the rest of us can step in and take over. We even have a word for it. It's called sisterhood.